As far as classic alpine scenery goes, the Tetons have the edge on the Gros Ventres. Since you're looking for 4-5 nights, I'd recommend the Teton Crest Trail (you'll need a shuttle). It will take you along Death Canyon Shelf, near Static Peak Divide, into Alaska Basin, to Hurricane Pass, and then into Cascade Canyon South Fork, where you shouldn't miss the spur to Avalanche Divide. Later, you can choose to head out via Cascade Canyon (shorter and easier) or take North Fork Cascade over Paintbrush Divide and down Paintbrush Canyon (longer and harder but absolutely spectacular).
Alaska Basin and parts of the Cascade Canyon area can be quite crowded, but by backpacking you can see the best things early and late in the day when there's little traffic. And the scenery is so good that the crowds are (somewhat) bearable.
A problem, though: you need permits to camp in the park, and they started accepting reservations back on January 1. You are now unlikely to get anything in the choice camping zones along this route by reserving them, leaving you to hope to get something in person the day before you start out.
Now, I personally like the Gros Ventres better because they are wilder, plenty rugged, and lightly used. And they are still jaw-droppingly beautiful, just not the same way the Tetons are. You need no permits, and there are lots of possibilities for long backcountry routes. If you want solitude and adventure, they'll do it for you. Some loops from Granite Creek near Hoback Junction: Granite Highline back around to Granite Hot Springs, Swift Creek and Shoal Falls back over Deer Ridge.